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This study investigates how anomalous resistivity affects tearing instability in magnetized plasmas by incorporating a second-order resistivity model into magnetohydrodynamic equations. The analysis reveals localized spatial singularities at critical boundaries that create unexpected jump conditions, leading to a hyperbolic, time-dependent growth rate that diverges before reaching saturation. The authors demonstrate that higher-order non-linear current feedback uniquely drives an explosive finite-time singularity, providing an analytical explanation for the abrupt onset of explosive magnetic reconnection events.
Why it matters
This research offers a theoretical solution to the long-standing "trigger problem" that explains the sudden onset of solar flares and tokamak disruptions in fusion devices. Understanding these explosive reconnection mechanisms could improve predictions of dangerous space weather events and enhance the safety and stability of fusion reactors by identifying early warning signatures of plasma instabilities.
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arXiv:2606.16363v1 Announce Type: cross
Abstract: We study the modification of classical tearing instability due to anomalous resistivity by incorporating a variable, second-order resistivity model into the resistive magnetohydrodynamics (MHD) framework. We evaluate the resulting multi-order perturbation modifications and boundary-layer scaling laws. By extending the perturbation analysis to second-order accuracy, we resolve localized spatial singularities ($delta$ and $delta’$) at the threshold boundary. These singularities generate unexpected matching jump conditions, demonstrating an early-stage phase-slip layer that forces a hyperbolic, time-dependent growth rate divergence prior to macroscopic saturation. Physical estimates for fusion devices and solar flares prove that this multi-order approach triggers an abrupt transition into the explosive reconnection regime, offering an exact analytical resolution to the long-standing solar and tokamak flare/disruption “trigger problem,” respectively. Finally, a comparative analysis using a truncated linear expansion of the threshold model regularizes the singular behavior, confirming that the explosive finite-time singularity is uniquely driven by the higher-order non-linear current feedback.
Source: The Effect of Anomalous Resistivity on Tearing Instability